Related Polytopes
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
t0(131) |
t0,1(131) |
t0,2(131) |
t0,3(131) |
t0,4(131) |
t0,1,2(131) |
t0,1,3(131) |
t0,1,4(131) |
t0,2,3(131) |
t0,2,4(131) |
t0,3,4(131) |
t0,1,2,3(131) |
t0,1,2,4(131) |
t0,1,3,4(131) |
t0,2,3,4(131) |
t0,1,2,3,4(131) |
The 6-demicube, 131 is third in a dimensional series of uniform polytopes, expressed by Coxeter as k31 series. The fifth figure is a Euclidean honeycomb, 331, and the final is a noncompact hyperbolic honeycomb, 431. Each progressive uniform polytope is constructed from the previous as its vertex figure.
| n | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|
| Coxeter group |
A3×A1 | A5 | D6 | E7 | = E7+ | E7++ |
| Coxeter diagram |
||||||
| Symmetry (order) |
(48) |
(720) |
(23,040) |
(2,903,040) |
(∞) |
(∞) |
| Graph | ∞ | ∞ | ||||
| Name | −131 | 031 | 131 | 231 | 331 | 431 |
It is also the second in a dimensional series of uniform polytopes and honeycombs, expressed by Coxeter as 13k series. The next figure is the Euclidean honeycomb 133 and the final is a noncompact hyperbolic honeycomb, 134.
| n | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|
| Coxeter group |
A3×A1 | A5 | D6 | E7 | =E7+ | E7++ |
| Coxeter diagram |
||||||
| Symmetry (order) |
(48) |
(720) |
(23,040) |
(2,903,040) |
] (∞) |
(∞) |
| Graph | ∞ | ∞ | ||||
| Name | 13,-1 | 130 | 131 | 132 | 133 | 134 |
Read more about this topic: 6-demicube
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